Frequency conversion in optically nonlinear crystals is typically used to generate laser-radiation at a wavelength shorter than that which can be generated directly as fundamental radiation in a particular laser type. One common frequency-conversion operation is generating radiation having a wavelength in the visible region of the electromagnetic spectrum from radiation having a having a wavelength in the near infrared (NIR) region of the electromagnetic spectrum.
By way of example, radiation from a laser having a fundamental wavelength of 1040 nanometers (nm) can be converted to radiation having a wavelength of 520 nm by second-harmonic generation (frequency-doubling) in an optically nonlinear crystal. The 520 nm radiation can be converted to shorter-wavelength radiation by further frequency-conversion steps. For example, frequency-doubling to provide radiation having a wavelength of 260 nm or third-harmonic generation by sum-frequency mixing the 520 nm radiation with the 1040 nm-radiation to provide radiation having a wavelength of about 347 nm.
A basic requirement of any frequency-conversion operation is that the beam of laser-radiation being frequency-converted and the beam of frequency-converted radiation both overlap and stay in phase for as long as possible within the optically nonlinear crystal. Cutting the crystal with a particular entrance-face angle with respect to the crystal axes is one way to keep the radiation beams in phase. This is usually referred to as “phase-matching” by practitioners of the art.
Optically nonlinear crystals are birefringent. The radiation being frequency-converted and the frequency-converted radiation are orthogonally polarized with respect to each other. Therefore, in a critical frequency-conversion arrangement, the radiation beams propagate at an angle to each other within the crystal. This divergence is typically referred to as “spatial walk-off” by practitioners of the art. The distance over which the radiation beams remain effectively overlapped depends on a particular crystal, a particular conversion operation, and the beam cross-section dimensions. Assuming the radiation being converted is either continuous-wave (CW) radiation or pulsed radiation having a pulse-duration of several picoseconds (ps) or greater, the beams can remain overlapped for distances of up to about 10 millimeters (mm) in the crystal. Two crystals can be arranged in series such that spatial walk-off in one crystal is at least partially compensated in the other. This is described in detail in U.S. Pat. No. 5,136,597, the complete disclosure of which is hereby incorporated by reference.
A problem arises when the laser-radiation being frequency converted is pulsed, having a pulse-duration of less than about a few hundred femtoseconds (fs). Pulses having a duration of between about 100 fs and about 200 fs are typically delivered by passively mode-locked fiber lasers. The wavelength being converted and the converted wavelength generally have different group velocities in the crystal, and the difference can be sufficient for pulses at the two different wavelengths to become temporally separated. This separation is typically referred to as “temporal walk-off” by practitioners of the art. The pulse being frequency converted may be faster than the frequency converted pulse or vice versa, depending again on a particular crystal and a particular conversion operation. Temporal walk-off limits the efficiency of frequency conversion and can distort the temporal pulse-shape of the frequency-converted radiation.
By way of example, in converting 1040 nm pulses to 520 nm pulses in lithium triborate (LBO), the inverse group velocity of the 1040 nm pulses (in the ordinary ray) is 5419.5 femtoseconds per millimeter (fs/mm). The inverse group velocity of the generated 520 nm pulses (in the extraordinary ray) is 5468.7 fs/mm. The difference between the inverse group velocities is 49.2 fs/mm, which means that a 1040 nm pulse and a corresponding 520 nm pulse will become temporally separated (at the half-peak intensity points) after propagating a distance of about 3 mm. This becomes essentially the maximum useful crystal length.
For such a short crystal, a high peak-intensity is required to obtain a useful conversion efficiency, about 10 Gigawatts per centimeter squared in the example. This is typically obtained by focusing a beam of radiation to be converted into a relatively small spot, having a diameter of about 100 micrometers (μm) in the example. Such a high peak-intensity, however, can lead to limited crystal lifetime. Crystal lifetime can be extended by using a crystal having relatively large lateral dimensions compared to the beam spot-size and shifting the crystal with respect to the beam, either periodically or continually. However, this requires precisely controllable translation stages, which add to apparatus cost.
Another relatively-elaborate approach to increasing conversion efficiency is to use multiple crystals arranged to compensate both temporal and spatial walk. Such an arrangement is describe in a paper “Simultaneous spatial and temporal walk-off compensation in frequency-doubling femtosecond pulses in β-BaB2O4”, Gehr et al., Optics letters, Vol. 23, No. 16, Aug. 15, 1998. This involves five optically nonlinear crystals, with three thereof actively frequency-doubling, interspersed with two passive compensating crystals. The five crystals are arranged to provide spatial and temporal walk-off compensation.
There is a need for temporal walk-off compensation for frequency converting femtosecond laser pulses in an optically nonlinear crystal. Preferably, the temporal walk-off compensation should be achieved without using an additional crystal.